Inference and Estimation for Population Parameters Quiz

Test your knowledge on point estimators, confidence intervals, hypothesis testing, and more in statistical inference.

Practice Learn Test

Which of the following is a point estimator for the population mean?

Sample mean

Sample variance

Population mean

Population variance

What is the relationship between sample size and the margin of error in a confidence interval?

Inverse relationship: as sample size increases, margin of error decreases

Inverse relationship: as sample size increases, margin of error increases

Direct relationship: as sample size increases, margin of error decreases

Direct relationship: as sample size increases, margin of error increases

In statistical hypothesis testing, what does the null hypothesis usually state?

The absence of an effect or difference

The presence of an effect or difference

The uncertainty of the estimate

The incorrectness of the estimate

What is the formula for calculating the coefficient of variation (CV)?

(Sample standard deviation / Sample mean) * 100

(Sample mean / Sample standard deviation) * 100

(Population standard deviation / Population mean) * 100

(Population mean / Population standard deviation) * 100

What is the standard error of the sample mean?

Sample variance divided by sample size

Sample size divided by sample variance

Population variance divided by population size

Population size divided by population variance

In hypothesis testing, what is the p-value?

The probability of committing a Type I error

The probability of rejecting a true null hypothesis

The probability of observing a sample statistic as extreme as, or more extreme than, the one observed

The probability of accepting the null hypothesis

What is the purpose of the Central Limit Theorem in statistics?

To define the center of a dataset

To provide a method for calculating confidence intervals

To describe the distribution of a sample mean, regardless of the original population distribution

To estimate population parameters directly

What does the term 'statistical power' refer to in hypothesis testing?

The probability of making a Type I error

The probability of making a Type II error

The likelihood of correctly rejecting a false null hypothesis

The likelihood of incorrectly accepting a true null hypothesis

What is the purpose of a Type I error in hypothesis testing?

To incorrectly reject a true null hypothesis

To incorrectly accept a false null hypothesis

To correctly reject a false null hypothesis

To correctly accept a true null hypothesis

#10

What is the formula for the confidence interval of the population mean?

Sample mean ± Z* × (Sample standard deviation / √sample size)

Sample mean ± t* × (Sample standard deviation / √sample size)

Sample mean ± Z* × (Population standard deviation / √population size)

Sample mean ± t* × (Population standard deviation / √population size)

#11

What is the purpose of bootstrapping in statistical inference?

To create more data points for analysis

To estimate the sampling distribution of a statistic by resampling with replacement from the observed data

To reduce the size of the dataset

To eliminate outliers from the dataset

#12

In regression analysis, what does the coefficient of determination (R-squared) represent?

The proportion of the dependent variable explained by the independent variable

The correlation coefficient between the variables

The probability of the model being accurate

The slope of the regression line

#13

What is the purpose of the standard normal distribution (Z-distribution) in statistical analysis?

To represent the distribution of a sample mean

To standardize normal distributions with different means and standard deviations

To calculate confidence intervals for proportions

To analyze categorical data

#14

What is the formula for calculating the margin of error in a confidence interval?

Z* × (Sample standard deviation / √sample size)

t* × (Sample standard deviation / √sample size)

Z* × (Population standard deviation / √population size)

t* × (Population standard deviation / √population size)